Correct Answer - Option 2 :
\(K=\dfrac{4EI}{L}\)
Explanation
Stiffness (k) is defined as the force per unit deflection or moment required per unit rotation.
Stiffness factor for a beam simply supported at both ends is 3EI/L
Important Points:
For the far end being Hinged Supported:
If a unit rotation is to be caused at an end A for the far end being hinged support. Moment of \(\frac{{3EI}}{L}\) is to be applied at end and hence stiffness for the member is said to be \(\frac{{3EI}}{L}.\)
For the far end being Fixed Supported:
If a unit rotation is to be caused at an end A for the far end being fixed supported. Moment of \(\frac{{4EI}}{L}\) is to be applied at end and hence stiffness for the member is said to be \(\frac{{4EI}}{L}.\)